I have a bunch of ordinal variables, but they have lots of categories and a ton of variability. For example, I have an income variable with 9 categories. Do you think it would be okay to treat that as interval in tests?
No matter what is the number of categories, ordinal variables cannot be classified as interval scale variables and hence we can't apply parametric stats on it
Can you give more examples? In the case of income, you can recode each category to its mid-point.
The income data are ratio data. If you use the real numbers, you can treat them as ratio/interval data. If you’re worried about observations to variables number, you can collapse the categories. Investigate the distribution and your research question before you collapse categories.
One last thing. Ordinal data is treated as interval data all the time--Likert scales being the most common example.
David Coker I would have concerns about treating single-item Likert-scored variables as interval. The more common practice is to assess whether multi-item scales can be combined into an interval-level variable.
I agree--treating single items on a questionnaire as a stand alone metric, while commonly done, is a poor practice. With that being said, an entire scale based off ordinal data is ordinal data, but most statisticians agree the data can be used for parametric research. The downside to transforming data, such as income, into categories is one loses data.
Sullivan, G. M., & Artino Jr, A. R. (2013). Analyzing and interpreting data from Likert-type scales. Journal of graduate medical education, 5(4), 541-542.
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